### Abstract

The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius eta, are studied in the small Prandtl number limit. When eta = O, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and O for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of convection of the linear stability of a fluid sphere containing a uniform distribution of heat sources. When an inner solid core is present (and eta is non-zero) all the modes of classes F and D persist outside C_{c} (where C_{c} is the coaxial cylinder whose generators touch the inner core at its equator) but the set E of modes (of both F and D) is suppressed within C_{c}.-Author

Original language | English |
---|---|

Pages (from-to) | 129-167 |

Number of pages | 39 |

Journal | Geophysical and Astrophysical Fluid Dynamics |

Volume | 16 |

Issue number | 1-2 |

Publication status | Published - 1980 |

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### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics
- Space and Planetary Science
- Computational Mechanics
- Mechanics of Materials
- Astronomy and Astrophysics

### Cite this

**On the propagation and stability of wave motions in rapidly rotating spherical shells. I. the non-magnetic case.** / Eltayeb, I. A.

Research output: Contribution to journal › Article

*Geophysical and Astrophysical Fluid Dynamics*, vol. 16, no. 1-2, pp. 129-167.

}

TY - JOUR

T1 - On the propagation and stability of wave motions in rapidly rotating spherical shells. I. the non-magnetic case.

AU - Eltayeb, I. A.

PY - 1980

Y1 - 1980

N2 - The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius eta, are studied in the small Prandtl number limit. When eta = O, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and O for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of convection of the linear stability of a fluid sphere containing a uniform distribution of heat sources. When an inner solid core is present (and eta is non-zero) all the modes of classes F and D persist outside Cc (where Cc is the coaxial cylinder whose generators touch the inner core at its equator) but the set E of modes (of both F and D) is suppressed within Cc.-Author

AB - The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius eta, are studied in the small Prandtl number limit. When eta = O, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and O for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of convection of the linear stability of a fluid sphere containing a uniform distribution of heat sources. When an inner solid core is present (and eta is non-zero) all the modes of classes F and D persist outside Cc (where Cc is the coaxial cylinder whose generators touch the inner core at its equator) but the set E of modes (of both F and D) is suppressed within Cc.-Author

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M3 - Article

AN - SCOPUS:0019193609

VL - 16

SP - 129

EP - 167

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 1-2

ER -